Problems and Failure Mechanisms
One of the first steps to a geotechnical engineering problem is to come up with all possible failure mechanisms and problems that must be considered for a successful design. By anticipating these problems and failure types, we can analyze them and ensure an adequate factor of safety or margin of safety against their occurrence. In this section we will look at the most common failure mechanisms and problems, but this is by no means an exhaustive list!
What Lies Beneath
Geotechnical engineers are intimately familiar with the tremendously variable nature of earth materials. It is challenging enough to come up with design parameters and implement a design for foundations on level ground. But sloping ground can be even worse. If the slope is natural, inadequate investigations may fail to discover a slide plane or bedding plane that has an unfavorable orientation or material properties that can lead to a global or overall stability failure. Or the steep terrain may make it difficult or costly to get good geotechnical data in the form of borings. In the case of existing fill slopes or embankments to be widened, most of the time there is not very good data available on the condition of those fill slopes, the material used, how well they were compacted during construction or what the fill/native contact looked like before the fill was constructed. Often times the top 1-2 ft of that interface can be poorly compacted, possibly creating a preferential slip plane. For new construction, compaction control for this interface zone should be a top priority.
“You Broke it, You Bought It”
Most people are familiar with that little adage I used to title this subsection. I think it is particularly appropriate when it comes to discussing side-hill retaining walls. In all of the cases I described in the previous subsection, the existing native or man-made slope is at least marginally stable. Now if you go and put a retaining wall perched on the slope, that slope becomes a part of your wall system but a part you have little or no control over. If any part of the slope under the wall fails, there goes your wall. It can become an interesting issue from the perspective of design but also it can be a huge liability for you and your company or agency!
Figure 3: Schematic diagram of lightweight concrete fill (LCF) used behind a CIP retaining wall to ensure no net increase in applied pressure to an existing slope. Image courtesy of NCS Consultants, LLC.
Global Stability and Compound Stability
The global stability or overall stability failure mode is frequently what controls the design of side-hill walls. The standard method of analysis would be a circular type failure surface passing behind the wall and exiting on the slope in front. But your analyses shouldn’t be limited to just circular failures, non-circular and block failure surfaces should be analyzed as well. In the case of MSE walls and reinforced soil slopes, compound failure surfaces passing between the reinforcement levels should be considered as well.
Obtaining accurate shear strength parameters from the field and laboratory investigation are critical before starting any slope stability analysis. Usually a factor of safety of 1.3 to 1.5 is the target value. Make sure your client understands that there is a world of difference (and frequently cost) associated with increasing the factor of safety from 1.3 to 1.5.
In my experience, this is where I spent a great deal of time during the analysis of side-hill walls, performing run after run of global stability analysis. It used to be in XSTABL, but now we do most of our work in SLOPE/W (we do?), part of the GeoStudio family of products. You have to be sure to pick a software program that has good search algorithms for finding the critical failure surface. That’s why we like SLOPE/W; they have an optimization feature where once you find your critical failure surface using a circular, non-circular or some other type of search, it tweaks each segment of the critical failure surface to see if the factor of safety lowers or not. It seems to do a fairly good job, and I find the resulting failure surfaces to look more realistic than what it started with. Of course, sometimes you get more than you bargained for!
One last word of caution, don’t simply use slope stability software as a black box, make sure you understand the inputs you are using and the options you are selecting and the limitations of the software and algorithms, especially with complicated programs like Slope/W. Make sure you choose an analysis method that considers both force and moment equilibrium. Use engineering judgment as to whether a total or effective stress analysis is warranted, and when in doubt, perform both.
Bearing Capacity / Bearing Resistance
Conventional bearing capacity theory covers flat ground. Once you go to sloping ground in front of the wall, you can look at a chart based solution that provides you with modified bearing capacity factors (Meyerhof, 1957; NAVFAC, 1986a, 1986b; and AASHTO) or you can try a rigorous numerical approach described in Bowles (1988). Note, that’s Bowles 4th Edition, the 5th Edition doesn’t have that solution. However, you may decide that running a slope stability analysis with carefully selected entry and exit points may be sufficient to analyze a bearing capacity type of failure. You can use surcharge loads to simulate the uniform bearing pressures from your wall foundation. (Figure 4: Sample global stability failure surface showing a bearing capacity type failure analysis on a side-hill retaining wall. From Morrison et. al. (2006), Shored Mechanically Stabilized Earth (SMSE) Wall Systems Design Guidelines)
Settlement
The significance of settlement for a side-hill retaining wall really depends on the type of wall system. For example, a wire-faced MSE wall will generally tolerate more settlements than a CIP wall. And differential settlements may be no big deal for a cantilevered soldier pile lagging wall (SPL wall), but if there are deadman anchors involved, too much differential settlement could snap the tie rods.
For a side-hill wall project involving both cantilevered and anchored SPL walls, we had decided to break up the triangular prism of new soil behind the wall into a series of strips and use an elastic solution for a uniform surcharge to determine the stress distribution at depth in order to compute settlements and differential settlements. A schematic diagram of this approach is shown below in Figure 5.
Figure 5: Modeling stress from triangular shaped prism using superimposed strip loads
Using this type of setup for a wall height of around 15-ft, you might compute something like what is shown in Figure 6. This Figure shows increased vertical stress as a function of depth at a location about 6-ft behind the wall, which is near where the maximum stress increase was computed as filling of the backfill progressed.
Figure 6: Increase in vertical stress as a function of depth at about 6-ft behind the wall
The previous figure shows how stress is varying with depth, but what about with distance from the wall? You would expect the stress increase and consequently the settlement to be greater where the height of new soil in the triangular prism is greatest (ie. right behind the wall). The resulting differential settlement compared with the other end of the triangle should be evaluated to determine if the wall system can handle the settlements. To see what I mean, take a look at Figure 7 which shows the variation of increased vertical stress along the X-Axis at a fixed depth corresponding to results of a superimposed strip load analysis with 15 strips. Again, this particular case had an exposed height of about 16-ft and included a deadman anchor at a depth of 6-ft.
Figure 7: Increase in vertical stress as a function of distance behind the wall at about 12-ft below the top of wall
Internal Stability
I was thinking of primarily MSE walls when I added this section. In addition to the above, global failure mechanisms, things like pullout resistance, reinforcement strength, connection strength and facing strength need to be considered. (Figure 8: Example of MSE wall reinforcement. Photo by Antonio Conte, ADOT via NCS Consultants, LLC.)
